Bold Tweets

Friday May 4, 2018 with all analysis

Data cleaning

congress = read.csv('more-data/all_w_IBM_50.csv')
# clean data - convert to numeric
congress[is.na(congress)] = 0
congress$gender = as.numeric(congress$gender)
congress$type = as.numeric(congress$type)
congress$party = as.numeric(congress$party)
congress

Take rates of tag

#round_ones = function(col){
#  col[col != 0] = 1
#  col
#}
#round_ones(congress$Joy)
congress$Sadness[congress$Sadness != 0] = 1
congress$Joy[congress$Joy != 0] = 1
congress$Tentative[congress$Tentative != 0] = 1
congress$Confident[congress$Confident != 0] = 1
congress$Analytical[congress$Analytical != 0] = 1
congress$Anger[congress$Anger != 0] = 1
congress$Fear[congress$Fear != 0] = 1
congress

Old style analysis

• tweets viewed as all \(y_i = ax_i + b\) with normally distributed error
• women more sad
• men more joyful
• women MAYBE more tentative
• women more analytical
• women more fearful

women_tweets = congress[congress$gender == 1,]
men_tweets = congress[congress$gender == 2,]
t.test(women_tweets$Sadness, men_tweets$Sadness) #, var.equal = TRUE)

    Welch Two Sample t-test

data:  women_tweets$Sadness and men_tweets$Sadness
t = 3.7961, df = 10593, p-value = 0.0001478
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.00915687 0.02870989
sample estimates:
 mean of x  mean of y 
0.08186916 0.06293578 

t.test(women_tweets$Joy, men_tweets$Joy)

    Welch Two Sample t-test

data:  women_tweets$Joy and men_tweets$Joy
t = -4.1526, df = 10793, p-value = 3.313e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.05229073 -0.01875445
sample estimates:
mean of x mean of y 
0.2540187 0.2895413 

t.test(women_tweets$Tentative, men_tweets$Tentative)

    Welch Two Sample t-test

data:  women_tweets$Tentative and men_tweets$Tentative
t = 1.4584, df = 10730, p-value = 0.1448
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.002009026  0.013686982
sample estimates:
 mean of x  mean of y 
0.04822430 0.04238532 

t.test(women_tweets$Analytical, men_tweets$Analytical)

    Welch Two Sample t-test

data:  women_tweets$Analytical and men_tweets$Analytical
t = 5.0816, df = 10675, p-value = 3.806e-07
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.02222660 0.05014243
sample estimates:
mean of x mean of y 
0.1820561 0.1458716 

t.test(women_tweets$Confident, men_tweets$Confident)

    Welch Two Sample t-test

data:  women_tweets$Confident and men_tweets$Confident
t = 1.185, df = 10761, p-value = 0.236
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.003708367  0.015046788
sample estimates:
 mean of x  mean of y 
0.06897196 0.06330275 

t.test(women_tweets$Fear, men_tweets$Fear)

    Welch Two Sample t-test

data:  women_tweets$Fear and men_tweets$Fear
t = 2.2784, df = 10208, p-value = 0.02272
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.0005934379 0.0079052331
sample estimates:
 mean of x  mean of y 
0.01158879 0.00733945 

t.test(women_tweets$Anger, men_tweets$Anger)

    Welch Two Sample t-test

data:  women_tweets$Anger and men_tweets$Anger
t = -0.38681, df = 10791, p-value = 0.6989
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.003724927  0.002497112
sample estimates:
  mean of x   mean of y 
0.006542056 0.007155963 

Retweets, Favorites

• yes women also favorited when confident, not as much as men (nearly significant)

visualize

dep = congress$tweet_favorite_count
w_tweets = dep[congress$gender == 1]
g = split(congress, congress$gender)
wom = split(g$`1`, g$`1`$Confident) # women
men = split(g$`2`, g$`2`$Confident) # men
one = wom$`0` # not conf women
two = wom$`1` # conf women
three = men$`0` # not conf men
four = men$`1` # conf men

f = function(dat){
  log(1+log(1+dat$tweet_favorite_count))#[dat$tweet_favorite_count>0]))
}
#congress$tweet_favorite_count>0
hist(f(congress), main='Favorites ~ Power Law', xlab='log log favorites')

barplot(c(mean(f(one)), mean(f(two)), mean(f(three)), mean(f(four))), names.arg=c('Women Neutral', 'Women Confident', 'Men Neutral', 'Men Confident'), main = 'Favorites vs. Confidence and Gender', ylab= 'log log favorite (mean)')

boxplot(f(one), f(two), f(three), f(four), ylab='log favorites', names = c('Women not conf', 'Women conf', 'Men not conf', 'Men conf'), main='Men more rewarded for confidence')

formalism

• all are more favorited when confident
• men more so than women

dep = f(congress)
mfav10 = lm(dep ~ congress$Confident + congress$gender) # both effects significant, women are favorited more
mfavint0 = lm(dep ~ congress$Confident * congress$gender)
anova(mfav10, mfavint0)

Analysis of Variance Table

Model 1: dep ~ congress$Confident + congress$gender
Model 2: dep ~ congress$Confident * congress$gender
  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1  10797 3986.1                              
2  10796 3984.7  1    1.4019 3.7983 0.05133 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• NOT SIG WHEN TAKE OUT ZERO-FAVORITES - maybe something to do with retweet status?

f = function(dat){
  log(1+log(1+dat$tweet_favorite_count[dat$tweet_favorite_count>0]))
}
#dep = log(1+congress$tweet_favorite_count)
fact = congress$tweet_favorite_count > 0
dep = f(congress)
mfav0 = lm(dep ~ congress$Confident[fact]) # positive, significant
mfav1 = lm(dep ~ congress$Confident[fact] + congress$gender[fact]) # both effects significant, women are favorited more
mfavint = lm(dep ~ congress$Confident[fact] * congress$gender[fact])
summary(mfav0)

Call:
lm(formula = dep ~ congress$Confident[fact])

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8680 -0.2417 -0.0116  0.2121  1.2159 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)              1.322110   0.003998 330.670  < 2e-16 ***
congress$Confident[fact] 0.072468   0.014816   4.891 1.02e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3595 on 8718 degrees of freedom
Multiple R-squared:  0.002737,  Adjusted R-squared:  0.002622 
F-statistic: 23.92 on 1 and 8718 DF,  p-value: 1.021e-06

summary(mfav1)

Call:
lm(formula = dep ~ congress$Confident[fact] + congress$gender[fact])

Residuals:
    Min      1Q  Median      3Q     Max 
-0.9186 -0.2413 -0.0144  0.2062  1.1791 

Coefficients:
                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)               1.477872   0.011982  123.34  < 2e-16 ***
congress$Confident[fact]  0.072262   0.014659    4.93 8.39e-07 ***
congress$gender[fact]    -0.104970   0.007622  -13.77  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3557 on 8717 degrees of freedom
Multiple R-squared:  0.02397,   Adjusted R-squared:  0.02375 
F-statistic: 107.1 on 2 and 8717 DF,  p-value: < 2.2e-16

summary(mfavint)

Call:
lm(formula = dep ~ congress$Confident[fact] * congress$gender[fact])

Residuals:
     Min       1Q   Median       3Q      Max 
-0.91199 -0.24071 -0.01492  0.20710  1.17969 

Coefficients:
                                                Estimate Std. Error t value
(Intercept)                                     1.479463   0.012394 119.367
congress$Confident[fact]                        0.050439   0.045884   1.099
congress$gender[fact]                          -0.106042   0.007916 -13.396
congress$Confident[fact]:congress$gender[fact]  0.014724   0.029338   0.502
                                               Pr(>|t|)    
(Intercept)                                      <2e-16 ***
congress$Confident[fact]                          0.272    
congress$gender[fact]                            <2e-16 ***
congress$Confident[fact]:congress$gender[fact]    0.616    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3557 on 8716 degrees of freedom
Multiple R-squared:  0.024, Adjusted R-squared:  0.02367 
F-statistic: 71.45 on 3 and 8716 DF,  p-value: < 2.2e-16

anova(mfav1, mfavint) # reject mfav1 at p~.05, means there is an interaction. NOT IF WE REMOVE ZERO-valued tweets!

Analysis of Variance Table

Model 1: dep ~ congress$Confident[fact] + congress$gender[fact]
Model 2: dep ~ congress$Confident[fact] * congress$gender[fact]
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1   8717 1102.8                           
2   8716 1102.8  1  0.031871 0.2519 0.6158

Are the zero-favorited tweets outliers?

#four$IBM_text[four$tweet_favorite_count==0]
5

[1] 5

New analysis: aggregate first

• note: I’m AM doing the nonzero->1 trick with IBM scores.
• be careful if you run in a certain order the above; the following analysis might change.

agged = aggregate(congress, by=list(congress$twitter), FUN=function(x) mean(as.numeric(x)))
                    #mean)
congress

agged

hi

women = agged[agged$gender == 1,]
women

men = agged[agged$gender == 2,]
men

#agged$Anger[agged$Anger != 0]

Gender diffs (or lack thereof) by plots

• Sadness, Joy, Analytical, Confident = not too sparse
• Tentative = borderline
• Fear, anger = too sparse

measure = "Politician IBM score (mean)"
shapiro.test(women$Joy) # not normally distributed

    Shapiro-Wilk normality test

data:  women$Joy
W = 0.97917, p-value = 0.09117

shapiro.test(women$Tentative)

    Shapiro-Wilk normality test

data:  women$Tentative
W = 0.91906, p-value = 6.638e-06

hist(women$Sadness)

hist(women$Joy, xlab=measure, main='Joy - Approximately normal (p > .05)')

hist(women$Tentative, xlab=measure, main='Tentative - Not approx. normal (p < 1e-05)')

hist(women$Analytical)

hist(women$Confident)

hist(women$Fear)

hist(women$Anger)

agged women against men plots

indep_col_1 = rgb(0,0,1,1/4)
indep_col_2 = rgb(1,0,0,1/4)
depw = women$Analytical
depm = men$Analytical
hist(depw, col=indep_col_1, main='Women as or more Analytical', xlab=measure)
hist(depm, col=indep_col_2, add=T)

legend1 = "Analytical - women"
legend2 = "Analytical - men"
legend(.25, 30, legend=c(legend1, legend2),
       col=c(indep_col_1, indep_col_2), lty=1, lwd=10, cex=0.8)

d = data.frame(women=depw, men=depm[1:107])
boxplot(d, main='Women as or more Analytical', ylab=measure)

#stripchart(d,
#            vertical = TRUE, #method = "jitter", 
#            pch = 21, col = "maroon", bg = "bisque",
#            add = TRUE) 
#hist(women$Sadness, col=indep_col_1)
#hist(men$Sadness, col=indep_col_2, add=T)
#plot(p1, col='blue')

d = data.frame(women_sad=women$Sadness, men_sad=men$Sadness[1:107], women_joy = women$Joy, men_joy = men$Joy[1:107])
boxplot(d, main='Women not more \"agreeable\"', ylab=measure, names = c("Women sad", "Men sad", "Women joy", "Men joy"))

d2 = data.frame(women_conf=women$Confident, men_conf = men$Confident[1:107], women_analytic=women$Analytical, men_analytic = men$Analytical[1:107])
boxplot(d2, main='Women as or more \"forceful\"', ylab=measure, names = c("Women conf", "Men conf", "Women analytical", "Men analytical"))

Numerical conclusions, correspond to above visuals

• women more sad
• Men more joy
• women more analytical
• can get confidence interval on women’s CONFIDENCE relative to men
• Women likely more fearful
• Similar anger

t.test(women$Sadness, men$Sadness) #, var.equal = TRUE)

    Welch Two Sample t-test

data:  women$Sadness and men$Sadness
t = 3.3452, df = 207.69, p-value = 0.0009757
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.007775157 0.030091601
sample estimates:
 mean of x  mean of y 
0.08186916 0.06293578 

t.test(women$Joy, men$Joy)

    Welch Two Sample t-test

data:  women$Joy and men$Joy
t = -2.6595, df = 212.49, p-value = 0.008422
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.061851649 -0.009193536
sample estimates:
mean of x mean of y 
0.2540187 0.2895413 

t.test(women$Tentative, men$Tentative)

    Welch Two Sample t-test

data:  women$Tentative and men$Tentative
t = 1.2482, df = 212.44, p-value = 0.2133
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.00338211  0.01506007
sample estimates:
 mean of x  mean of y 
0.04822430 0.04238532 

t.test(women$Analytical, men$Analytical)

    Welch Two Sample t-test

data:  women$Analytical and men$Analytical
t = 3.8041, df = 214, p-value = 0.0001857
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.01743531 0.05493372
sample estimates:
mean of x mean of y 
0.1820561 0.1458716 

x = t.test(women$Confident, men$Confident)
x

    Welch Two Sample t-test

data:  women$Confident and men$Confident
t = 1.0942, df = 209.23, p-value = 0.2751
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.004544338  0.015882759
sample estimates:
 mean of x  mean of y 
0.06897196 0.06330275 

x$conf.int

[1] -0.004544338  0.015882759
attr(,"conf.level")
[1] 0.95

x$estimate

 mean of x  mean of y 
0.06897196 0.06330275 

# t.test(women$Confident, men$Confident, alternative = 'greater')
t.test(women$Fear, men$Fear)

    Welch Two Sample t-test

data:  women$Fear and men$Fear
t = 2.0704, df = 209.34, p-value = 0.03965
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.0002031941 0.0082954769
sample estimates:
 mean of x  mean of y 
0.01158879 0.00733945 

t.test(women$Anger, men$Anger)

    Welch Two Sample t-test

data:  women$Anger and men$Anger
t = -0.32948, df = 209.51, p-value = 0.7421
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.004287036  0.003059222
sample estimates:
  mean of x   mean of y 
0.006542056 0.007155963 

Robustness

• fuller models into party, age.

• sad women remains stat sig even with party; some small evidence for involving the fuller model with an additive party or interacted party.

msad1 = lm(agged$Sadness ~ agged$gender)
msad11 = lm(agged$Sadness ~ agged$party)
msad111 = lm(agged$Sadness ~ agged$age)
#plot(msad111)
#plot(agged$age, agged$Sadness)
#abline(msad111)
summary(msad1)

Call:
lm(formula = agged$Sadness ~ agged$gender)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.081869 -0.022936 -0.002936  0.018131  0.158131 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.100803   0.008961   11.25  < 2e-16 ***
agged$gender -0.018933   0.005652   -3.35 0.000955 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.04153 on 214 degrees of freedom
Multiple R-squared:  0.04983,   Adjusted R-squared:  0.04539 
F-statistic: 11.22 on 1 and 214 DF,  p-value: 0.000955

# model involving party:
msad2 = lm(agged$Sadness ~ agged$gender + agged$party)
summary(msad2)

Call:
lm(formula = agged$Sadness ~ agged$gender + agged$party)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.08392 -0.02486 -0.00392  0.02016  0.15608 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.107996   0.010538  10.248  < 2e-16 ***
agged$gender -0.016239   0.006016  -2.699  0.00751 ** 
agged$party  -0.007838   0.006067  -1.292  0.19781    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.04146 on 213 degrees of freedom
Multiple R-squared:  0.05722,   Adjusted R-squared:  0.04836 
F-statistic: 6.463 on 2 and 213 DF,  p-value: 0.001883

anova(msad1, msad2)

Analysis of Variance Table

Model 1: agged$Sadness ~ agged$gender
Model 2: agged$Sadness ~ agged$gender + agged$party
  Res.Df     RSS Df Sum of Sq      F Pr(>F)
1    214 0.36909                           
2    213 0.36622  1 0.0028694 1.6689 0.1978

• Men more joy is not robust to party. Republicans are more joyful given Trump, naturally.
• age not needed

mjoy1 = lm(agged$Joy ~ agged$gender)
mjoy2 = lm(agged$Joy ~ agged$gender + agged$party)
mjoy3 = lm(agged$Joy ~ agged$gender + agged$party + agged$age)
summary(mjoy1)

Call:
lm(formula = agged$Joy ~ agged$gender)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.209541 -0.074019  0.005981  0.067101  0.290459 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.21850    0.02120  10.307  < 2e-16 ***
agged$gender  0.03552    0.01337   2.657  0.00848 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09824 on 214 degrees of freedom
Multiple R-squared:  0.03193,   Adjusted R-squared:  0.02741 
F-statistic: 7.059 on 1 and 214 DF,  p-value: 0.00848

summary(mjoy2)

Call:
lm(formula = agged$Joy ~ agged$gender + agged$party)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.19160 -0.06070 -0.00516  0.06840  0.32128 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.17177    0.02428   7.074 2.14e-11 ***
agged$gender  0.01802    0.01386   1.300 0.195027    
agged$party   0.05090    0.01398   3.641 0.000341 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09554 on 213 degrees of freedom
Multiple R-squared:  0.08866,   Adjusted R-squared:  0.08011 
F-statistic: 10.36 on 2 and 213 DF,  p-value: 5.078e-05

summary(mjoy3)

Call:
lm(formula = agged$Joy ~ agged$gender + agged$party + agged$age)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.20419 -0.06417 -0.00175  0.06619  0.32427 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.2249574  0.0487494   4.615 6.82e-06 ***
agged$gender  0.0177069  0.0138458   1.279  0.20234    
agged$party   0.0466853  0.0143583   3.251  0.00134 ** 
agged$age    -0.0007777  0.0006184  -1.258  0.20991    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09541 on 212 degrees of freedom
Multiple R-squared:  0.09541,   Adjusted R-squared:  0.08261 
F-statistic: 7.454 on 3 and 212 DF,  p-value: 9.084e-05

anova(mjoy1, mjoy2)

Analysis of Variance Table

Model 1: agged$Joy ~ agged$gender
Model 2: agged$Joy ~ agged$gender + agged$party
  Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
1    214 2.0654                                  
2    213 1.9444  1   0.12104 13.259 0.0003406 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

anova(mjoy2, mjoy3)

Analysis of Variance Table

Model 1: agged$Joy ~ agged$gender + agged$party
Model 2: agged$Joy ~ agged$gender + agged$party + agged$age
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1    213 1.9444                           
2    212 1.9300  1  0.014399 1.5816 0.2099

• Democrats more analytical, women still stat significant
• interactions not needed, age not needed.

mAnalytical1 = lm(agged$Analytical ~ agged$gender)
mAnalytical2 = lm(agged$Analytical ~ agged$gender + agged$party)
mAnalytical3 = lm(agged$Analytical ~ agged$gender * agged$party)
mAnalytical4 = lm(agged$Analytical ~ agged$gender + agged$party + agged$age)
summary(mAnalytical1)

Call:
lm(formula = agged$Analytical ~ agged$gender)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.162056 -0.043010 -0.005872  0.037944  0.214128 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.218241   0.015084  14.469  < 2e-16 ***
agged$gender -0.036185   0.009513  -3.804 0.000186 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.06991 on 214 degrees of freedom
Multiple R-squared:  0.06332,   Adjusted R-squared:  0.05894 
F-statistic: 14.47 on 1 and 214 DF,  p-value: 0.0001861

summary(mAnalytical2)

Call:
lm(formula = agged$Analytical ~ agged$gender + agged$party)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.153177 -0.049106 -0.009106  0.048627  0.188395 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.257248   0.017075  15.066  < 2e-16 ***
agged$gender -0.021573   0.009748  -2.213    0.028 *  
agged$party  -0.042499   0.009830  -4.323 2.36e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.06718 on 213 degrees of freedom
Multiple R-squared:  0.1389,    Adjusted R-squared:  0.1308 
F-statistic: 17.18 on 2 and 213 DF,  p-value: 1.214e-07

anova(mAnalytical1, mAnalytical2)

Analysis of Variance Table

Model 1: agged$Analytical ~ agged$gender
Model 2: agged$Analytical ~ agged$gender + agged$party
  Res.Df     RSS Df Sum of Sq     F    Pr(>F)    
1    214 1.04579                                 
2    213 0.96143  1  0.084364 18.69 2.361e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# interactions not needed.
anova(mAnalytical2, mAnalytical3)

Analysis of Variance Table

Model 1: agged$Analytical ~ agged$gender + agged$party
Model 2: agged$Analytical ~ agged$gender * agged$party
  Res.Df     RSS Df Sum of Sq      F Pr(>F)
1    213 0.96143                           
2    212 0.95975  1 0.0016767 0.3704 0.5435

anova(mAnalytical2, mAnalytical4)

Analysis of Variance Table

Model 1: agged$Analytical ~ agged$gender + agged$party
Model 2: agged$Analytical ~ agged$gender + agged$party + agged$age
  Res.Df     RSS Df Sum of Sq      F Pr(>F)
1    213 0.96143                           
2    212 0.95964  1 0.0017855 0.3944 0.5307

• party does not help explain the non-result of confidence.

mConfident0 = lm(agged$Confident ~ agged$party)
mConfident1 = lm(agged$Confident ~ agged$gender)
mConfident2 = lm(agged$Confident ~ agged$gender + agged$party)
mConfident3 = lm(agged$Confident ~ agged$gender * agged$party)
mConfident4 = lm(agged$Confident ~ agged$gender + agged$party + agged$age)
summary(mConfident0)

Call:
lm(formula = agged$Confident ~ agged$party)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.067705 -0.027705 -0.004043  0.015957  0.115957 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.071367   0.007937   8.992   <2e-16 ***
agged$party -0.003662   0.005227  -0.701    0.484    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.03809 on 214 degrees of freedom
Multiple R-squared:  0.002289,  Adjusted R-squared:  -0.002373 
F-statistic: 0.4909 on 1 and 214 DF,  p-value: 0.4843

summary(mConfident1)

Call:
lm(formula = agged$Confident ~ agged$gender)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.068972 -0.028972 -0.003303  0.016697  0.116697 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.074641   0.008204   9.098   <2e-16 ***
agged$gender -0.005669   0.005175  -1.096    0.274    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.03802 on 214 degrees of freedom
Multiple R-squared:  0.005578,  Adjusted R-squared:  0.0009309 
F-statistic:   1.2 on 1 and 214 DF,  p-value: 0.2745

summary(mConfident2)

Call:
lm(formula = agged$Confident ~ agged$gender + agged$party)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.069472 -0.029472 -0.003504  0.017451  0.115541 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.076394   0.009684   7.889 1.58e-13 ***
agged$gender -0.005013   0.005528  -0.907    0.366    
agged$party  -0.001910   0.005575  -0.343    0.732    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0381 on 213 degrees of freedom
Multiple R-squared:  0.006125,  Adjusted R-squared:  -0.003207 
F-statistic: 0.6563 on 2 and 213 DF,  p-value: 0.5198

anova(mConfident1, mConfident2)

Analysis of Variance Table

Model 1: agged$Confident ~ agged$gender
Model 2: agged$Confident ~ agged$gender + agged$party
  Res.Df     RSS Df  Sum of Sq      F Pr(>F)
1    214 0.30940                            
2    213 0.30923  1 0.00017033 0.1173 0.7323

# interactions not needed.
anova(mConfident2, mConfident3)

Analysis of Variance Table

Model 1: agged$Confident ~ agged$gender + agged$party
Model 2: agged$Confident ~ agged$gender * agged$party
  Res.Df     RSS Df  Sum of Sq      F Pr(>F)
1    213 0.30923                            
2    212 0.30916  1 6.9315e-05 0.0475 0.8276

anova(mConfident2, mConfident4)

Analysis of Variance Table

Model 1: agged$Confident ~ agged$gender + agged$party
Model 2: agged$Confident ~ agged$gender + agged$party + agged$age
  Res.Df     RSS Df  Sum of Sq      F Pr(>F)
1    213 0.30923                            
2    212 0.30830  1 0.00092298 0.6347 0.4265

# HELLO, SAVE!